Question

Let S = {a,b,c} and T= {1,2,3}.
Find \(F^{-1}\) of the following functions F from S to T, if it exists.
 I. F={(a,3),(b,2),(c,1)} 
 II. F={(a,2),(b,1),(c,1)}

Answer 1

S = {a, b, c}, T = {1, 2, 3} 
(i) F: S \(\to\) T is defined as: 
F = {(a, 3), (b, 2), (c, 1)} 
\(\Rightarrow\) F (a) = 3, F (b) = 2, F(c) = 1 
Therefore, F−1: T \(\to\) S is given by 
\(F^{-1}\) = {(3, a), (2, b), (1, c)}. 

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(ii) F: S \(\to\) T is defined as: 
F = {(a, 2), (b, 1), (c, 1)} 
Since F (b) = F (c) = 1, 
F is not one-one. 

Hence, F is not invertible i.e., \(F^{-1}\) does not exist.